Question

For a Boolean function f(x, y, z)...
(a) DNF = CNF = f(x, y, z)
(b) f(x, y, z) = DNF only
(c) f(x, y, z) = CNF only
(d) DNF and CNF are complements of ea
For a function f(x, y, z) defined as​

Answer 1

Answer:

,Therefore, the DNF of f is: xyz'+ xy'z+xy'z'+xyz'. Method of Putting a Function in CNF, using Truth Tables: 1. Create the truth table of the given ...

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Answer 2

Answer:

• A Boolean function is a mathematic expression (B,+, . , ‘, 0,1) where B is a non-empty set and they are binary operations in B
• In other words, a Boolean function is a function whose arguments and result assume values from a two-element set
• The results can be true or false, 0 or 1

The properties are :

a) + and . are communative: for all x and y in B, x+y=y+x, and x.y=y.x

b) + and . are associative: for all x, y and z in B, x+(y+z)=(x+y)+z, and x.(y.z)=(x.y).z

c) + and . are distributive to each other: x.(y+z)=xy+xz, and x+(y.z)=(x+y).(x+z)

d) Other is the Identity laws where 1.x=x.1=x and 0+x=x+0=x for all x in B

e) Complementation laws: x+x’=1 and x.x’=0 for all x in B

Boolean expressions are of 2 types

1. Disjunctive Normal Form: A Boolean function/expression is in Disjunctive Normal Form (DNF). It is also called minterm canonical form, if the function/expression is a sum of minterms.

Examples:

1. f(x,y,z)= xyz+xy’z+x’yz’+x’y’z is in DNF
2. g(x,y)=xy+x’y’ is in DNF

2. Conjunctive Normal Form : A Boolean function/expression is in Conjunctive Normal Form (CNF). It is also called maxterm canonical form, if the function/expression is a product of maxterms.

Examples:

1. f(x,y,z)= (x+y+z)(x+y+z’)(x’+y+z’)(x’+y’+z) is in CNF
2. g(x,y)=(x+y)(x’+y’) is in CNF

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